Find all of the solutions of the equation x^4-625i=0 and represent the solutions graphically.

Answer 1

(x^2-25√i)(x^2+25√i)
(x-5∜i)(x+5∜i)(x-5∜i i)(x+5∜i i)

Now just use de Moivre's formulas to find ∜i.

If you want, you can rephrase these solutions as

±5(-1)^(1/8)
±5(-1)^(5/8)